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Proof step 11 from proof scale-not-neg (previous step)

i % 10 = 0, mkDecimal(i / 10, abs(i0) - 1).scale < 0, ∀ i1, i0. i→n(i1) < i→n(i) → mkDecimal(i1, i0).scale < 0 → false ⊦ i = 0, i0 = 0

User applied rule apply induction

And closed the goal!

Rule argument

subst: [i1, i0] → [i / 10, abs(i0) - 1]

Additional information

Used simplifier rules: labs: ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); from specification intnat%abs: j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j); from specification int-div%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%abs-div10-le: ⊦ abs(i) ≤ abs(i) / 10 ↔ i = 0; from specification int-div Used terms: i / 10, abs(i0) - 1